Infinite dimensional families of Calabi–Yau threefolds and moduli of vector bundles

Ballico, Edoardo; Gasparim, Elizabeth; Suzuki, Bruno

doi:10.1016/j.jpaa.2020.106554

Cited by 8 publications

(1 citation statement)

References 12 publications

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“…A conjecture of Yau states that the topological type of (connected, smooth, compact) Calabi-Yau manifolds is finite in every dimension (we already see this in complex dimensions 1 and 2) and it could well be that 960 is the upper bound in dimension 3. There has been nice parallel directions of work in infinite families of Calabi-Yaus [52,53] beyond topological type such as Gromow-Witten invariants, as well as in zooming in on special corners of small Hodge numbers [41][42][43].…”

Section: Reflexive Polytopesmentioning

confidence: 99%

Universes as big data

2021

Int. J. Mod. Phys. A

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In this paper, we briefly overview how, historically, string theory led theoretical physics first to precise problems in algebraic and differential geometry, and thence to computational geometry in the last decade or so, and now, in the last few years, to data science. Using the Calabi–Yau landscape — accumulated by the collaboration of physicists, mathematicians and computer scientists over the last four decades — as a starting-point and concrete playground, we review some recent progress in machine-learning applied to the sifting through of possible universes from compactification, as well as wider problems in geometrical engineering of quantum field theories. In parallel, we discuss the program in machine-learning mathematical structures and address the tantalizing question of how it helps doing mathematics, ranging from mathematical physics, to geometry, to representation theory, to combinatorics and to number theory.

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